[KneeCo]

Can we assume the following about hand 1?

1) We are ahead on this flop more often than not.
2) If we check behind Deeb will probably bet the turn.
3) There are 21 cards, and accordingly a ~44% chance of seeing one of them, on the turn that would make us cringe.
4) Where we are ahead, Deeb has outs (2 or more) to take the lead, and in most cases will be taking the lead with a hand that he knows is best. There is nothing about this hand that makes the old adage about never giving a draw a free card moot.
5) Getting check raised is possible, but so is taking the pot down with a flop bet.

As best I can tell, none of these assumptions are especially controversial, if we accept them, I think it's clear that betting the flop is best.